Question Use scientific notation to determine which of these numbers is greater: 34,835,760 or 43,835,760. Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

Answer 1

To compare the numbers 34,835,760 and 43,835,760 using scientific notation, we first convert each number into scientific notation.

1. For 34,835,760:

   To convert this to scientific notation, we need to express it in the form \( a \times 10^n \), where 1 ≤ a < 10.

   \[ 34,835,760 = 3.4835760 \times 10^7 \]

2. For 43,835,760:

   Similarly, we convert this number:

   \[ 43,835,760 = 4.3835760 \times 10^7 \]

Now we have:

• \( 34,835,760 \) in scientific notation is \( 3.4835760 \times 10^7 \).
• \( 43,835,760 \) in scientific notation is \( 4.3835760 \times 10^7 \).

Now, we can compare the two numbers. Since both numbers are in scientific notation with the same exponent \( 10^7 \), we only need to compare the coefficients:

• \( 3.4835760 \) (from the first number)
• \( 4.3835760 \) (from the second number)

Clearly, \( 4.3835760 > 3.4835760 \).

Therefore, the greater number is:

\[ 43,835,760 = 4.3835760 \times 10^7 \]

Thus, in scientific notation, the greater number is:

\[ \boxed{4.3835760 \times 10^7} \]

Answer 2

write it regularly in scintific notation

Answer 3

The number 43,835,760 can be expressed in regular scientific notation by simplifying it. Scientific notation is typically presented with one non-zero digit to the left of the decimal point.

For \(43,835,760\):

1. Move the decimal point 7 places to the left: \[ 4.3835760 \rightarrow 4.383576 \times 10^7 \]

In regular scientific notation, it is standard to limit the number of decimal places. To express this in scientific notation with three decimal places, it would be:

\[ \boxed{4.384 \times 10^7} \]

This is the proper way to write the number 43,835,760 in scientific notation, rounded to three decimal places.

Answer 4

Use scientific notation to determine which of these numbers has the least value: 123,893, 31,892, or 12,786. Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

Answer 5

To determine which of the numbers 123,893, 31,892, or 12,786 has the least value using scientific notation, we first convert each number into scientific notation.

1. For 123,893: \[ 123,893 = 1.23893 \times 10^5 \]

2. For 31,892: \[ 31,892 = 3.1892 \times 10^4 \]

3. For 12,786: \[ 12,786 = 1.2786 \times 10^4 \]

Now, we have the scientific notation for each number:

• \( 123,893 \) is \( 1.23893 \times 10^5 \)
• \( 31,892 \) is \( 3.1892 \times 10^4 \)
• \( 12,786 \) is \( 1.2786 \times 10^4 \)

Now, we can compare these values based on the powers of ten:

• \( 1.23893 \times 10^5 \) (which is \( 123,893 \)): This has an exponent of 5.
• \( 3.1892 \times 10^4 \) (which is \( 31,892 \)): This has an exponent of 4.
• \( 1.2786 \times 10^4 \) (which is \( 12,786 \)): This also has an exponent of 4.

Since \( 10^5 \) is greater than \( 10^4 \), we can conclude that both \( 31,892 \) and \( 12,786 \) will be compared directly as they share the same exponent.

Now, comparing \( 3.1892 \) (for \( 31,892 \)) and \( 1.2786 \) (for \( 12,786 \)), we can see that:

\[ 1.2786 < 3.1892 \]

Thus, \( 12,786 \) is the smallest number.

In scientific notation, the least value among the given numbers is:

\[ \boxed{1.2786 \times 10^4} \]